Metric spaces and textures

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DOST Ş.

APPLIED GENERAL TOPOLOGY, vol.18, no.1, pp.203-217, 2017 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.4995/agt.2017.6889
  • Journal Name: APPLIED GENERAL TOPOLOGY
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.203-217
  • Hacettepe University Affiliated: Yes

Abstract

Textures are point-set setting for fuzzy sets, and they provide a framework for the complement-free mathematical concepts. Further dimetric on textures is a generalization of classical metric spaces. The aim of this paper is to give some properties of dimetric texture space by using categorical approach. We prove that the category of classical metric spaces is isomorphic to a full subcategory of dimetric texture spaces, and give a natural transformation from metric topologies to dimetric ditopologies. Further, it is presented a relation between dimetric texture spaces and quasi -pseudo metric spaces in the sense of J. F. Kelly.